Logarithm Rules, Tables, Formulas and Shortcuts

Logarithm Solved Examples - Page 3
Logarithm Important Questions - Page 4
Logarithm Video Lecture - Page 5

Logarithm, in mathematics is the exponent or power to which a stated number called base , is raised to yield a specific number. For example on the expression $10^{2}\, =\, 100$, the Logarithm of 100 to the base 10 is 2. This is written as $Log_{10}\, 100\, =\, 2$ Logarithms were originally invented to help simplify the arithmetical processes of multiplication, division, expansion to a power and extraction of a 'root', but they are now a days used for variety of purposes in pure and applied mathematics.

If for a positive real number (a ≠ 1) , $a^{m}\, =\, b$, then the index m is called the Logarithm of b to the base a.
We write this as: $Log_{a}b\, m$
Log begins the abbreviation of the word ‘Logarithm’. Thus $a^{m}\, b\, \leftrightarrow \, log_{a}b\, =\, m$
Where $a^{m}$ = b is called the exponential form and $Log_{a}b\, =\, m$ is called the Logarithmic form.

Exponential Form
$3^{5}\, =\, 243$
$2^{4}\, =\, 16$
$3^{0}\, =\, 1$
$8^{\frac{1}{3}}\, =\, 2$

Logarithmic Form

$log_{3}243\, =\, 5$
$log_{2}16\, =\, 4$
$log_{3}1\, =\, 0$
$log_{8}2\, =\, \frac{1}{3}$